value of integration , Mathematics

Assignment Help:

what is the value of integration limit n-> infinity [n!/n to the power n]to the power 1/n

Solution)  limit n-->inf.    [1 + (n!-n^n)/n^n]^1/n

= e^ limit n-->inf.    {(n!-n^n)/n^n}.1/n         

                             (applying formula lim x-->a  [1 + f(x)]^g(x) =    e ^ {lim x-->a    f(x).g(x)}  )

=e ^ lim n-->inf.       (n-1)!/(n)^n-1   -   1/n

=e ^ lim n---> inf.     (1-1/n)(1-2/n)(1-3/n)......1/n   -    1/n

=e ^ (1-o)(1-0).....(1-0).0  -   0

=e ^ 0-0

=1

hence, integation 1= x + C

 

 


Related Discussions:- value of integration

Multiple integrals, how to convert multiple integral into polar form and ch...

how to convert multiple integral into polar form and change the limits of itegration

Explain how we converting fractions to percents, Explain how we Converting ...

Explain how we Converting Fractions to Percents ? To convert a fraction to a percent: 1. Convert the fraction to a decimal using long division. 2. Move the decimal point two p

Determine the function f ( x ) , Determine the function f ( x ) .       ...

Determine the function f ( x ) .             f ′ ( x )= 4x 3 - 9 + 2 sin x + 7e x , f (0) = 15 Solution The first step is to integrate to fine out the most general pos

Calculus, f(x)= 2e^5x+6 find the domain of f and find x-intercept.

f(x)= 2e^5x+6 find the domain of f and find x-intercept.

Union operations using union by weight, Show the result of the following se...

Show the result of the following sequence of UNION operations using union-by-weight with the following assumptions Unions are performed on the representatives on the sets th

the volume of a pyramid, Write a script to determine the volume of a pyram...

Write a script to determine the volume of a pyramid, which is 1/3 * base * height, where the base is length * width.  On time the user to enter values for the length, width, and th

Vectors, why minimum three coplanar vectors are required to give zero resul...

why minimum three coplanar vectors are required to give zero resultant and not two?

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd